## for data
import pandas as pd
import numpy as np
## for plotting
import matplotlib.pyplot as plt
import seaborn as sns
## for statistical tests
import scipy
import statsmodels.formula.api as smf
import statsmodels.api as sm
## for machine learning
from sklearn import model_selection, preprocessing, feature_selection, ensemble, linear_model, metrics, decomposition
df=pd.read_csv('fundamentals.csv')
df.columns
Index(['Unnamed: 0', 'Ticker Symbol', 'Period Ending', 'Accounts Payable',
'Accounts Receivable', 'Add'l income/expense items', 'After Tax ROE',
'Capital Expenditures', 'Capital Surplus', 'Cash Ratio',
'Cash and Cash Equivalents', 'Changes in Inventories', 'Common Stocks',
'Cost of Revenue', 'Current Ratio', 'Deferred Asset Charges',
'Deferred Liability Charges', 'Depreciation',
'Earnings Before Interest and Tax', 'Earnings Before Tax',
'Effect of Exchange Rate',
'Equity Earnings/Loss Unconsolidated Subsidiary', 'Fixed Assets',
'Goodwill', 'Gross Margin', 'Gross Profit', 'Income Tax',
'Intangible Assets', 'Interest Expense', 'Inventory', 'Investments',
'Liabilities', 'Long-Term Debt', 'Long-Term Investments',
'Minority Interest', 'Misc. Stocks', 'Net Borrowings', 'Net Cash Flow',
'Net Cash Flow-Operating', 'Net Cash Flows-Financing',
'Net Cash Flows-Investing', 'Net Income', 'Net Income Adjustments',
'Net Income Applicable to Common Shareholders',
'Net Income-Cont. Operations', 'Net Receivables', 'Non-Recurring Items',
'Operating Income', 'Operating Margin', 'Other Assets',
'Other Current Assets', 'Other Current Liabilities', 'Other Equity',
'Other Financing Activities', 'Other Investing Activities',
'Other Liabilities', 'Other Operating Activities',
'Other Operating Items', 'Pre-Tax Margin', 'Pre-Tax ROE',
'Profit Margin', 'Quick Ratio', 'Research and Development',
'Retained Earnings', 'Sale and Purchase of Stock',
'Sales, General and Admin.',
'Short-Term Debt / Current Portion of Long-Term Debt',
'Short-Term Investments', 'Total Assets', 'Total Current Assets',
'Total Current Liabilities', 'Total Equity', 'Total Liabilities',
'Total Liabilities & Equity', 'Total Revenue', 'Treasury Stock',
'For Year', 'Earnings Per Share', 'Estimated Shares Outstanding'],
dtype='object')
df.head()
| Unnamed: 0 | Ticker Symbol | Period Ending | Accounts Payable | Accounts Receivable | Add'l income/expense items | After Tax ROE | Capital Expenditures | Capital Surplus | Cash Ratio | ... | Total Current Assets | Total Current Liabilities | Total Equity | Total Liabilities | Total Liabilities & Equity | Total Revenue | Treasury Stock | For Year | Earnings Per Share | Estimated Shares Outstanding | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0 | AAL | 2012-12-31 | 3.068000e+09 | -222000000.0 | -1.961000e+09 | 23.0 | -1.888000e+09 | 4.695000e+09 | 53.0 | ... | 7.072000e+09 | 9.011000e+09 | -7.987000e+09 | 2.489100e+10 | 1.690400e+10 | 2.485500e+10 | -367000000.0 | 2012.0 | -5.60 | 3.350000e+08 |
| 1 | 1 | AAL | 2013-12-31 | 4.975000e+09 | -93000000.0 | -2.723000e+09 | 67.0 | -3.114000e+09 | 1.059200e+10 | 75.0 | ... | 1.432300e+10 | 1.380600e+10 | -2.731000e+09 | 4.500900e+10 | 4.227800e+10 | 2.674300e+10 | 0.0 | 2013.0 | -11.25 | 1.630222e+08 |
| 2 | 2 | AAL | 2014-12-31 | 4.668000e+09 | -160000000.0 | -1.500000e+08 | 143.0 | -5.311000e+09 | 1.513500e+10 | 60.0 | ... | 1.175000e+10 | 1.340400e+10 | 2.021000e+09 | 4.120400e+10 | 4.322500e+10 | 4.265000e+10 | 0.0 | 2014.0 | 4.02 | 7.169154e+08 |
| 3 | 3 | AAL | 2015-12-31 | 5.102000e+09 | 352000000.0 | -7.080000e+08 | 135.0 | -6.151000e+09 | 1.159100e+10 | 51.0 | ... | 9.985000e+09 | 1.360500e+10 | 5.635000e+09 | 4.278000e+10 | 4.841500e+10 | 4.099000e+10 | 0.0 | 2015.0 | 11.39 | 6.681299e+08 |
| 4 | 4 | AAP | 2012-12-29 | 2.409453e+09 | -89482000.0 | 6.000000e+05 | 32.0 | -2.711820e+08 | 5.202150e+08 | 23.0 | ... | 3.184200e+09 | 2.559638e+09 | 1.210694e+09 | 3.403120e+09 | 4.613814e+09 | 6.205003e+09 | -27095000.0 | 2012.0 | 5.29 | 7.328355e+07 |
5 rows × 79 columns
df.dtypes
Unnamed: 0 int64
Ticker Symbol object
Period Ending object
Accounts Payable float64
Accounts Receivable float64
...
Total Revenue float64
Treasury Stock float64
For Year float64
Earnings Per Share float64
Estimated Shares Outstanding float64
Length: 79, dtype: object
df.isnull().sum()
Unnamed: 0 0
Ticker Symbol 0
Period Ending 0
Accounts Payable 0
Accounts Receivable 0
...
Total Revenue 0
Treasury Stock 0
For Year 173
Earnings Per Share 219
Estimated Shares Outstanding 219
Length: 79, dtype: int64
#Missing values
def display_missing_perc(df):
for col in df.columns.tolist():
print(f'{col} column missing values: {100*(df[col].isnull().sum()/len(df[col]))}')
print('\n')
display_missing_perc(df)
Unnamed: 0 column missing values: 0.0 Ticker Symbol column missing values: 0.0 Period Ending column missing values: 0.0 Accounts Payable column missing values: 0.0 Accounts Receivable column missing values: 0.0 Add'l income/expense items column missing values: 0.0 After Tax ROE column missing values: 0.0 Capital Expenditures column missing values: 0.0 Capital Surplus column missing values: 0.0 Cash Ratio column missing values: 16.78832116788321 Cash and Cash Equivalents column missing values: 0.0 Changes in Inventories column missing values: 0.0 Common Stocks column missing values: 0.0 Cost of Revenue column missing values: 0.0 Current Ratio column missing values: 16.78832116788321 Deferred Asset Charges column missing values: 0.0 Deferred Liability Charges column missing values: 0.0 Depreciation column missing values: 0.0 Earnings Before Interest and Tax column missing values: 0.0 Earnings Before Tax column missing values: 0.0 Effect of Exchange Rate column missing values: 0.0 Equity Earnings/Loss Unconsolidated Subsidiary column missing values: 0.0 Fixed Assets column missing values: 0.0 Goodwill column missing values: 0.0 Gross Margin column missing values: 0.0 Gross Profit column missing values: 0.0 Income Tax column missing values: 0.0 Intangible Assets column missing values: 0.0 Interest Expense column missing values: 0.0 Inventory column missing values: 0.0 Investments column missing values: 0.0 Liabilities column missing values: 0.0 Long-Term Debt column missing values: 0.0 Long-Term Investments column missing values: 0.0 Minority Interest column missing values: 0.0 Misc. Stocks column missing values: 0.0 Net Borrowings column missing values: 0.0 Net Cash Flow column missing values: 0.0 Net Cash Flow-Operating column missing values: 0.0 Net Cash Flows-Financing column missing values: 0.0 Net Cash Flows-Investing column missing values: 0.0 Net Income column missing values: 0.0 Net Income Adjustments column missing values: 0.0 Net Income Applicable to Common Shareholders column missing values: 0.0 Net Income-Cont. Operations column missing values: 0.0 Net Receivables column missing values: 0.0 Non-Recurring Items column missing values: 0.0 Operating Income column missing values: 0.0 Operating Margin column missing values: 0.0 Other Assets column missing values: 0.0 Other Current Assets column missing values: 0.0 Other Current Liabilities column missing values: 0.0 Other Equity column missing values: 0.0 Other Financing Activities column missing values: 0.0 Other Investing Activities column missing values: 0.0 Other Liabilities column missing values: 0.0 Other Operating Activities column missing values: 0.0 Other Operating Items column missing values: 0.0 Pre-Tax Margin column missing values: 0.0 Pre-Tax ROE column missing values: 0.0 Profit Margin column missing values: 0.0 Quick Ratio column missing values: 16.78832116788321 Research and Development column missing values: 0.0 Retained Earnings column missing values: 0.0 Sale and Purchase of Stock column missing values: 0.0 Sales, General and Admin. column missing values: 0.0 Short-Term Debt / Current Portion of Long-Term Debt column missing values: 0.0 Short-Term Investments column missing values: 0.0 Total Assets column missing values: 0.0 Total Current Assets column missing values: 0.0 Total Current Liabilities column missing values: 0.0 Total Equity column missing values: 0.0 Total Liabilities column missing values: 0.0 Total Liabilities & Equity column missing values: 0.0 Total Revenue column missing values: 0.0 Treasury Stock column missing values: 0.0 For Year column missing values: 9.713644020213364 Earnings Per Share column missing values: 12.296462661426165 Estimated Shares Outstanding column missing values: 12.296462661426165
#dropping NA values
df = df.dropna()
# Checking again for missing values
def display_missing_perc(df):
for col in df.columns.tolist():
print(f'{col} column missing values: {100*(df[col].isnull().sum()/len(df[col]))}')
print('\n')
display_missing_perc(df)
1. Data Exploration and Visualization
# Dropping specified columns
columns_to_drop = ['Ticker Symbol', 'Unnamed: 0', 'Period Ending','Estimated Shares Outstanding' ]
df_modified = df.drop(columns=columns_to_drop)
#scatterplots
# Scatter plot for R&D expenses vs. Earnings Per Share
plt.figure(figsize=(10, 6))
plt.scatter(df_modified['Research and Development'], df_modified['Earnings Per Share'])
plt.xlabel('Research and Development Expenses')
plt.ylabel('Earnings Per Share')
plt.title('R&D Expenses vs. Earnings Per Share')
plt.show()
# Scatter plot for Total Revenue vs. Net Income
plt.figure(figsize=(10, 6))
plt.scatter(df['Total Revenue'], df['Net Income'])
plt.xlabel('Total Revenue')
plt.ylabel('Net Income')
plt.title('Total Revenue vs. Net Income')
plt.show()
#Histograms
# Histogram for Earnings Per Share
plt.figure(figsize=(10, 6))
plt.hist(df['Earnings Per Share'], bins=20, edgecolor='black')
plt.xlabel('Earnings Per Share')
plt.ylabel('Frequency')
plt.title('Distribution of Earnings Per Share')
plt.show()
# Histogram for Gross Margin
plt.figure(figsize=(10, 6))
plt.hist(df['Gross Margin'], bins=20, edgecolor='black')
plt.xlabel('Gross Margin')
plt.ylabel('Frequency')
plt.title('Distribution of Gross Margin')
plt.show()
"""
R&D Expenses vs. EPS:
No clear linear relationship.
R&D spending alone doesn't predict EPS.
Total Revenue vs. Net Income:
Revenue increase doesn't guarantee proportional Net Income.
Some companies have losses despite high revenue.
EPS Distribution:
Majority of companies have low EPS.
Few high performing companies with high EPS.
Outliers on both ends.
Gross Margin Distribution:
Multimodal with peaks around 30 to 40.
Varies among companies or products
"""
cor=df_modified.corr()
plt.figure(figsize=(60,40))
sns.heatmap(data=cor,annot=True,cmap='Blues',fmt='.1g')
plt.show()
2. Linear Regression model Development: Creating linear regression to predict Estimated Shares Outstanding.
x = sm.add_constant(df_modified)
y = df['Estimated Shares Outstanding']
model = sm.OLS(y, x).fit()
print(model.summary())
OLS Regression Results
========================================================================================
Dep. Variable: Estimated Shares Outstanding R-squared: 0.854
Model: OLS Adj. R-squared: 0.846
Method: Least Squares F-statistic: 98.40
Date: Thu, 18 Jan 2024 Prob (F-statistic): 0.00
Time: 00:42:40 Log-Likelihood: -27507.
No. Observations: 1299 AIC: 5.516e+04
Df Residuals: 1225 BIC: 5.554e+04
Df Model: 73
Covariance Type: nonrobust
=======================================================================================================================
coef std err t P>|t| [0.025 0.975]
-----------------------------------------------------------------------------------------------------------------------
const 7.312e+08 1e+09 0.729 0.466 -1.24e+09 2.7e+09
Accounts Payable -183.9454 238.959 -0.770 0.442 -652.760 284.869
Accounts Receivable -0.0722 0.057 -1.274 0.203 -0.183 0.039
Add'l income/expense items 0.0361 0.057 0.635 0.525 -0.075 0.148
After Tax ROE -6.663e+05 5e+05 -1.332 0.183 -1.65e+06 3.15e+05
Capital Expenditures 0.9122 2.396 0.381 0.704 -3.789 5.614
Capital Surplus 0.0149 0.009 1.631 0.103 -0.003 0.033
Cash Ratio 6.866e+05 3.83e+05 1.793 0.073 -6.45e+04 1.44e+06
Cash and Cash Equivalents -1.2388 0.617 -2.008 0.045 -2.449 -0.029
Changes in Inventories -0.0876 0.060 -1.456 0.146 -0.206 0.030
Common Stocks -0.0014 0.010 -0.143 0.886 -0.020 0.018
Cost of Revenue 2439.1786 3340.878 0.730 0.465 -4115.298 8993.656
Current Ratio -2.044e+05 2.94e+05 -0.695 0.487 -7.82e+05 3.73e+05
Deferred Asset Charges -0.0585 0.989 -0.059 0.953 -1.999 1.882
Deferred Liability Charges 0.0094 0.099 0.095 0.925 -0.185 0.204
Depreciation -0.0843 0.057 -1.488 0.137 -0.196 0.027
Earnings Before Interest and Tax 22.5389 39.533 0.570 0.569 -55.022 100.100
Earnings Before Tax -22.8602 39.533 -0.578 0.563 -100.420 54.699
Effect of Exchange Rate -0.0233 0.166 -0.141 0.888 -0.348 0.302
Equity Earnings/Loss Unconsolidated Subsidiary 0.1119 0.082 1.371 0.171 -0.048 0.272
Fixed Assets -0.0572 0.989 -0.058 0.954 -1.998 1.883
Goodwill -0.0642 0.989 -0.065 0.948 -2.005 1.876
Gross Margin -1.512e+05 7.36e+05 -0.205 0.837 -1.6e+06 1.29e+06
Gross Profit 2439.1756 3340.878 0.730 0.465 -4115.301 8993.652
Income Tax 0.1562 0.067 2.342 0.019 0.025 0.287
Intangible Assets -0.0544 0.989 -0.055 0.956 -1.995 1.886
Interest Expense -22.8104 39.533 -0.577 0.564 -100.371 54.750
Inventory -1.2548 0.618 -2.030 0.043 -2.467 -0.042
Investments 0.8973 2.397 0.374 0.708 -3.805 5.600
Liabilities -0.0624 0.052 -1.194 0.233 -0.165 0.040
Long-Term Debt 0.0347 0.099 0.351 0.725 -0.159 0.229
Long-Term Investments -0.0746 0.989 -0.075 0.940 -2.015 1.866
Minority Interest 0.0162 0.100 0.162 0.872 -0.181 0.213
Misc. Stocks 0.3430 0.136 2.516 0.012 0.075 0.610
Net Borrowings 0.1033 0.021 5.022 0.000 0.063 0.144
Net Cash Flow 0.0538 0.087 0.617 0.537 -0.117 0.225
Net Cash Flow-Operating 0.0198 0.056 0.350 0.726 -0.091 0.131
Net Cash Flows-Financing -0.2019 0.091 -2.225 0.026 -0.380 -0.024
Net Cash Flows-Investing -0.9362 2.399 -0.390 0.696 -5.643 3.770
Net Income 0.2294 0.203 1.129 0.259 -0.169 0.628
Net Income Adjustments -0.0835 0.053 -1.565 0.118 -0.188 0.021
Net Income Applicable to Common Shareholders -0.1929 0.198 -0.974 0.330 -0.582 0.196
Net Income-Cont. Operations 0.1151 0.062 1.844 0.065 -0.007 0.237
Net Receivables -1.2667 0.617 -2.052 0.040 -2.478 -0.055
Non-Recurring Items 0.0457 0.022 2.097 0.036 0.003 0.088
Operating Income 0.1820 0.058 3.147 0.002 0.069 0.295
Operating Margin -8.032e+06 2.05e+06 -3.916 0.000 -1.21e+07 -4.01e+06
Other Assets -0.0390 0.989 -0.039 0.969 -1.980 1.902
Other Current Assets -1.2380 0.618 -2.004 0.045 -2.450 -0.026
Other Current Liabilities -183.9494 238.959 -0.770 0.442 -652.763 284.865
Other Equity 0.0057 0.012 0.465 0.642 -0.018 0.030
Other Financing Activities 0.0729 0.034 2.170 0.030 0.007 0.139
Other Investing Activities 0.8695 2.397 0.363 0.717 -3.833 5.572
Other Liabilities 0.0333 0.099 0.336 0.737 -0.161 0.227
Other Operating Activities -0.0985 0.057 -1.721 0.086 -0.211 0.014
Other Operating Items 0.0266 0.025 1.055 0.292 -0.023 0.076
Pre-Tax Margin 9.413e+06 2.77e+06 3.402 0.001 3.99e+06 1.48e+07
Pre-Tax ROE 4.397e+05 3.39e+05 1.295 0.196 -2.26e+05 1.11e+06
Profit Margin -3.036e+06 2.99e+06 -1.016 0.310 -8.9e+06 2.83e+06
Quick Ratio -3.744e+05 4.43e+05 -0.845 0.398 -1.24e+06 4.95e+05
Research and Development 0.0826 0.022 3.719 0.000 0.039 0.126
Retained Earnings -0.0097 0.009 -1.075 0.283 -0.027 0.008
Sale and Purchase of Stock 0.1254 0.021 5.960 0.000 0.084 0.167
Sales, General and Admin. 0.0127 0.013 0.940 0.347 -0.014 0.039
Short-Term Debt / Current Portion of Long-Term Debt -183.8769 238.959 -0.769 0.442 -652.692 284.938
Short-Term Investments -1.2200 0.617 -1.977 0.048 -2.431 -0.009
Total Assets 0.0386 0.992 0.039 0.969 -1.907 1.984
Total Current Assets 1.2034 1.160 1.037 0.300 -1.073 3.480
Total Current Liabilities 183.9484 238.959 0.770 0.442 -284.867 652.763
Total Equity -66.2225 94.133 -0.704 0.482 -250.901 118.456
Total Liabilities -66.2674 94.134 -0.704 0.482 -250.950 118.415
Total Liabilities & Equity 66.2613 94.135 0.704 0.482 -118.422 250.945
Total Revenue -2439.1795 3340.878 -0.730 0.465 -8993.656 4115.297
Treasury Stock -0.0074 0.009 -0.807 0.420 -0.025 0.011
For Year -2.385e+05 4.97e+05 -0.480 0.631 -1.21e+06 7.36e+05
Earnings Per Share -3.087e+07 2.81e+06 -10.983 0.000 -3.64e+07 -2.54e+07
==============================================================================
Omnibus: 1262.725 Durbin-Watson: 1.564
Prob(Omnibus): 0.000 Jarque-Bera (JB): 238833.428
Skew: 3.999 Prob(JB): 0.00
Kurtosis: 68.944 Cond. No. 1.17e+16
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.17e+16. This might indicate that there are
strong multicollinearity or other numerical problems.
# Dependent Variable : "Estimated Shares Outstanding" is the dependent variable, meaning the model is trying to predict it based on other factors. # R squared (0.854) : This indicates that 85.4% of the variability in the dependent variable can be explained by the model. # F statistic (98.40) : A high F statistic value suggests that the model is statistically significant.
P-Value Analysis with the histogram P-Value Analysis and Histogram: Creating a histogram of the p-values. To check ,If there any skewedness?
plt.hist(model.pvalues, bins=20, edgecolor='black')
plt.title('Histogram for P-Values')
plt.xlabel('P-Value')
plt.ylabel('Frequency')
plt.show()
The histogram shows three main groups of p-values: The first group is very close to zero. This suggests that some of the variables in the model are good at predicting the outcome since low p-values indicate significance. The second group is around the middle of the scale, near 0.4. This suggests that some variables may not be very good at predicting the outcome because their p-values are not low enough to be considered significant. The third group is close to 1. This suggests that some of the variables are not at all good at predicting the outcome, as high p-values indicate no significance. a bit left skewed
False Discovery Rate Control with BH Procedure Given the p values , use the BH procedure to control the FDR with a q of 0.1. How many “true” discoveries do you estimate?
pvals = model.pvalues
def fdr(pvals, q, plotit=False):
# Remove NA values
pvals = np.array(pvals)
pvals = pvals[~np.isnan(pvals)]
N = len(pvals)
# Sort the p-values and calculate the FDR threshold
sorted_pvals = np.sort(pvals)
k = np.arange(1, N+1)
fdr_threshold = (q * k) / N
# Find the last p-value that is below the FDR threshold
below_threshold = sorted_pvals <= fdr_threshold
max_index = np.max(np.where(below_threshold)) if np.any(below_threshold) else 0
alpha = sorted_pvals[max_index]
print(f"Alpha: {alpha}")
if plotit:
plt.scatter(range(N), sorted_pvals, c=np.where(sorted_pvals <= alpha, 'red', 'grey'), marker='o')
plt.yscale('log')
plt.plot(range(N), fdr_threshold, linestyle='--', color='blue')
plt.xlabel("Tests ordered by p-value")
plt.ylabel("p-values")
plt.title(f"FDR = {q}")
plt.show()
# Calculate the number of true discoveries
true_discoveries = sorted_pvals[sorted_pvals <= alpha]
num_of_true_discoveries = len(true_discoveries)
return num_of_true_discoveries, alpha
num_of_true_discoveries, alpha = fdr(model.pvalues, 0.1, plotit=True)
print(f"No. of true discoveries: {num_of_true_discoveries}")
Alpha: 0.001686631337479228
No. of true discoveries: 7
6. Sensitivity Analysis of FDR Control: If you apply the BH procedure at different q values, how do the results change? What does this tell you about the robustness of your significant variables?
q_values = [0.05, 0.1, 0.15, 0.2, 0.25]
# Placeholder for results
results = []
for q in q_values:
num_true_discoveries, alpha = fdr(model.pvalues, q, plotit=True)
results.append((q, num_true_discoveries, alpha))
# Print out the results
for result in results:
q, num_true_discoveries, alpha = result
print(f"When q= {q} \n"
f"The alpha is: {alpha} \n"
f"The estimated number of true discovery is: {num_true_discoveries}")
Alpha: 0.001686631337479228
Alpha: 0.001686631337479228
Alpha: 0.012009465808974997
Alpha: 0.026230280820006037
Alpha: 0.04826867981680562
When q= 0.05 The alpha is: 0.001686631337479228 The estimated number of true discovery is: 7 When q= 0.1 The alpha is: 0.001686631337479228 The estimated number of true discovery is: 7 When q= 0.15 The alpha is: 0.012009465808974997 The estimated number of true discovery is: 8 When q= 0.2 The alpha is: 0.026230280820006037 The estimated number of true discovery is: 10 When q= 0.25 The alpha is: 0.04826867981680562 The estimated number of true discovery is: 17
"""Here the estimated number of true discoveries grows as the q-value increases, particularly within the 0.05 to 0.10 range. A "drastic increase" is noted at a q-value of 0.2. the number of true discoveries jumps to 5 at a q-value of 0.15 and remains constant at 5 for higher q-values of 0.2 and 0.25. This suggests stability in the number of true discoveries once the q-value reaches 0.15 or above """
[a] Exploring Interaction Terms
variables = [
'Accounts Payable',
'Accounts Receivable',
'Add\'l income/expense items',
'After Tax ROE',
'Capital Expenditures',
'Capital Surplus',
'Cash Ratio',
'Cash and Cash Equivalents',
'Changes in Inventories',
'Common Stocks',
'Cost of Revenue',
'Current Ratio',
'Deferred Asset Charges',
'Deferred Liability Charges',
'Depreciation',
'Earnings Before Interest and Tax',
'Earnings Before Tax',
'Effect of Exchange Rate',
'Equity Earnings/Loss Unconsolidated Subsidiary',
'Fixed Assets',
'Goodwill',
'Gross Margin',
'Gross Profit',
'Income Tax',
'Intangible Assets'
]
df_modified2 = df[variables]
df_modified2.head()
| Accounts Payable | Accounts Receivable | Add'l income/expense items | After Tax ROE | Capital Expenditures | Capital Surplus | Cash Ratio | Cash and Cash Equivalents | Changes in Inventories | Common Stocks | ... | Earnings Before Interest and Tax | Earnings Before Tax | Effect of Exchange Rate | Equity Earnings/Loss Unconsolidated Subsidiary | Fixed Assets | Goodwill | Gross Margin | Gross Profit | Income Tax | Intangible Assets | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 3.068000e+09 | -222000000.0 | -1.961000e+09 | 23.0 | -1.888000e+09 | 4.695000e+09 | 53.0 | 1.330000e+09 | 0.0 | 127000000.0 | ... | -1.813000e+09 | -2.445000e+09 | 0.0 | 0.0 | 1.340200e+10 | 0.000000e+00 | 58.0 | 1.435600e+10 | -5.690000e+08 | 8.690000e+08 |
| 1 | 4.975000e+09 | -93000000.0 | -2.723000e+09 | 67.0 | -3.114000e+09 | 1.059200e+10 | 75.0 | 2.175000e+09 | 0.0 | 5000000.0 | ... | -1.324000e+09 | -2.180000e+09 | 0.0 | 0.0 | 1.925900e+10 | 4.086000e+09 | 59.0 | 1.572400e+10 | -3.460000e+08 | 2.311000e+09 |
| 2 | 4.668000e+09 | -160000000.0 | -1.500000e+08 | 143.0 | -5.311000e+09 | 1.513500e+10 | 60.0 | 1.768000e+09 | 0.0 | 7000000.0 | ... | 4.099000e+09 | 3.212000e+09 | 0.0 | 0.0 | 2.308400e+10 | 4.091000e+09 | 63.0 | 2.703000e+10 | 3.300000e+08 | 2.240000e+09 |
| 3 | 5.102000e+09 | 352000000.0 | -7.080000e+08 | 135.0 | -6.151000e+09 | 1.159100e+10 | 51.0 | 1.085000e+09 | 0.0 | 6000000.0 | ... | 5.496000e+09 | 4.616000e+09 | 0.0 | 0.0 | 2.751000e+10 | 4.091000e+09 | 73.0 | 2.989400e+10 | -2.994000e+09 | 2.249000e+09 |
| 4 | 2.409453e+09 | -89482000.0 | 6.000000e+05 | 32.0 | -2.711820e+08 | 5.202150e+08 | 23.0 | 5.981110e+08 | -260298000.0 | 7000.0 | ... | 6.579150e+08 | 6.240740e+08 | 0.0 | 0.0 | 1.292547e+09 | 7.638900e+07 | 50.0 | 3.098036e+09 | 2.364040e+08 | 2.884500e+07 |
5 rows × 25 columns
# degree=2 for interaction terms
polynomial_fea = PolynomialFeatures(degree=2, include_bias=False)
# fit and transform the data to create the interaction terms
interaction_fit = polynomial_fea.fit_transform(df_modified2)
# feature names for the columns from the Polynomial Features
interaction_features= polynomial_fea.get_feature_names_out(df_modified2.columns)
# interaction terms into DataFrame
interactions_df = pd.DataFrame(interaction_fit, columns=interaction_features)
interactions_df
| Accounts Payable | Accounts Receivable | Add'l income/expense items | After Tax ROE | Capital Expenditures | Capital Surplus | Cash Ratio | Cash and Cash Equivalents | Changes in Inventories | Common Stocks | ... | Gross Margin^2 | Gross Margin Gross Profit | Gross Margin Income Tax | Gross Margin Intangible Assets | Gross Profit^2 | Gross Profit Income Tax | Gross Profit Intangible Assets | Income Tax^2 | Income Tax Intangible Assets | Intangible Assets^2 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 3.068000e+09 | -222000000.0 | -1.961000e+09 | 23.0 | -1.888000e+09 | 4.695000e+09 | 53.0 | 1.330000e+09 | 0.0 | 127000000.0 | ... | 3364.0 | 8.326480e+11 | -3.300200e+10 | 5.040200e+10 | 2.060947e+20 | -8.168564e+18 | 1.247536e+19 | 3.237610e+17 | -4.944610e+17 | 7.551610e+17 |
| 1 | 4.975000e+09 | -93000000.0 | -2.723000e+09 | 67.0 | -3.114000e+09 | 1.059200e+10 | 75.0 | 2.175000e+09 | 0.0 | 5000000.0 | ... | 3481.0 | 9.277160e+11 | -2.041400e+10 | 1.363490e+11 | 2.472442e+20 | -5.440504e+18 | 3.633816e+19 | 1.197160e+17 | -7.996060e+17 | 5.340721e+18 |
| 2 | 4.668000e+09 | -160000000.0 | -1.500000e+08 | 143.0 | -5.311000e+09 | 1.513500e+10 | 60.0 | 1.768000e+09 | 0.0 | 7000000.0 | ... | 3969.0 | 1.702890e+12 | 2.079000e+10 | 1.411200e+11 | 7.306209e+20 | 8.919900e+18 | 6.054720e+19 | 1.089000e+17 | 7.392000e+17 | 5.017600e+18 |
| 3 | 5.102000e+09 | 352000000.0 | -7.080000e+08 | 135.0 | -6.151000e+09 | 1.159100e+10 | 51.0 | 1.085000e+09 | 0.0 | 6000000.0 | ... | 5329.0 | 2.182262e+12 | -2.185620e+11 | 1.641770e+11 | 8.936512e+20 | -8.950264e+19 | 6.723161e+19 | 8.964036e+18 | -6.733506e+18 | 5.058001e+18 |
| 4 | 2.409453e+09 | -89482000.0 | 6.000000e+05 | 32.0 | -2.711820e+08 | 5.202150e+08 | 23.0 | 5.981110e+08 | -260298000.0 | 7000.0 | ... | 2500.0 | 1.549018e+11 | 1.182020e+10 | 1.442250e+09 | 9.597827e+18 | 7.323881e+17 | 8.936285e+16 | 5.588685e+16 | 6.819073e+15 | 8.320340e+14 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 1294 | 2.255000e+08 | -40400000.0 | -3.480000e+07 | 11.0 | -3.423000e+08 | 4.330700e+09 | 166.0 | 1.083300e+09 | -164600000.0 | 2700000.0 | ... | 5329.0 | 2.504265e+11 | 1.607460e+10 | 4.405550e+10 | 1.176833e+19 | 7.553961e+17 | 2.070307e+18 | 4.848804e+16 | 1.328907e+17 | 3.642122e+17 |
| 1295 | 4.320000e+08 | -56100000.0 | -2.750000e+07 | 1.0 | -4.341000e+08 | 8.195300e+09 | 100.0 | 1.459300e+09 | -205400000.0 | 3000000.0 | ... | 4900.0 | 2.938040e+11 | 4.900000e+08 | 6.122410e+11 | 1.761649e+19 | 2.938040e+16 | 3.670997e+19 | 4.900000e+13 | 6.122410e+16 | 7.649776e+19 |
| 1296 | 1.381000e+09 | -99000000.0 | 9.000000e+06 | 54.0 | -1.840000e+08 | 8.780000e+08 | 43.0 | 6.100000e+08 | -178000000.0 | 5000000.0 | ... | 3969.0 | 1.821960e+11 | 1.178100e+10 | 5.058900e+10 | 8.363664e+18 | 5.408040e+17 | 2.322276e+18 | 3.496900e+16 | 1.501610e+17 | 6.448090e+17 |
| 1297 | 1.071000e+09 | 69000000.0 | -7.000000e+06 | 44.0 | -1.800000e+08 | 9.580000e+08 | 81.0 | 8.820000e+08 | -110000000.0 | 5000000.0 | ... | 4096.0 | 1.963520e+11 | 1.491200e+10 | 4.652800e+10 | 9.412624e+18 | 7.148440e+17 | 2.230436e+18 | 5.428900e+16 | 1.693910e+17 | 5.285290e+17 |
| 1298 | 1.313000e+09 | -58000000.0 | -8.100000e+07 | 32.0 | -2.240000e+08 | 1.012000e+09 | 65.0 | 1.154000e+09 | -262000000.0 | 5000000.0 | ... | 4096.0 | 1.937280e+11 | 1.318400e+10 | 7.616000e+10 | 9.162729e+18 | 6.235620e+17 | 3.602130e+18 | 4.243600e+16 | 2.451400e+17 | 1.416100e+18 |
1299 rows × 350 columns
import statsmodels.api as sm
x = sm.add_constant(interaction_df.reset_index(drop=True))
y = df['Estimated Shares Outstanding'].reset_index(drop=True)
interaction_model = sm.OLS(list(y), x).fit()
print(interaction_model.summary())
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.944
Model: OLS Adj. R-squared: 0.926
Method: Least Squares F-statistic: 52.58
Date: Thu, 18 Jan 2024 Prob (F-statistic): 0.00
Time: 02:05:16 Log-Likelihood: -26886.
No. Observations: 1299 AIC: 5.440e+04
Df Residuals: 983 BIC: 5.604e+04
Df Model: 315
Covariance Type: nonrobust
===================================================================================================================================================
coef std err t P>|t| [0.025 0.975]
---------------------------------------------------------------------------------------------------------------------------------------------------
const 0.0004 0.000 1.659 0.098 -6.75e-05 0.001
Accounts Payable -0.0737 0.046 -1.604 0.109 -0.164 0.016
Accounts Receivable -0.5023 0.284 -1.767 0.078 -1.060 0.056
Add'l income/expense items 0.0819 0.275 0.297 0.766 -0.458 0.622
After Tax ROE 0.0010 0.001 1.812 0.070 -8.12e-05 0.002
Capital Expenditures 0.0206 0.097 0.213 0.831 -0.169 0.210
Capital Surplus 0.0558 0.021 2.663 0.008 0.015 0.097
Cash Ratio -0.0006 0.000 -1.480 0.139 -0.001 0.000
Cash and Cash Equivalents -0.0262 0.059 -0.442 0.659 -0.142 0.090
Changes in Inventories -0.1714 0.497 -0.345 0.730 -1.148 0.805
Common Stocks -0.0120 0.049 -0.242 0.809 -0.109 0.085
Cost of Revenue -0.0081 0.009 -0.895 0.371 -0.026 0.010
Current Ratio -0.0002 0.000 -1.252 0.211 -0.001 0.000
Deferred Asset Charges 0.2457 0.121 2.025 0.043 0.008 0.484
Deferred Liability Charges -0.0335 0.059 -0.572 0.568 -0.149 0.082
Depreciation 0.0539 0.152 0.356 0.722 -0.244 0.351
Earnings Before Interest and Tax 0.3886 0.288 1.347 0.178 -0.177 0.955
Earnings Before Tax -0.4390 0.280 -1.568 0.117 -0.988 0.110
Effect of Exchange Rate -0.0015 0.024 -0.063 0.950 -0.049 0.046
Equity Earnings/Loss Unconsolidated Subsidiary -0.1952 0.123 -1.589 0.112 -0.436 0.046
Fixed Assets 0.0084 0.020 0.430 0.667 -0.030 0.047
Goodwill 0.0615 0.029 2.148 0.032 0.005 0.118
Gross Margin -0.0001 0.000 -0.465 0.642 -0.001 0.000
Gross Profit 0.0277 0.089 0.311 0.756 -0.147 0.203
Income Tax 0.2726 0.299 0.912 0.362 -0.314 0.859
Intangible Assets -0.1614 0.045 -3.625 0.000 -0.249 -0.074
Accounts Payable^2 4.115e-12 1.92e-12 2.144 0.032 3.48e-13 7.88e-12
Accounts Payable Accounts Receivable 5.646e-12 1.72e-11 0.329 0.742 -2.8e-11 3.93e-11
Accounts Payable Add'l income/expense items 4.613e-11 4.59e-11 1.006 0.315 -4.39e-11 1.36e-10
Accounts Payable After Tax ROE 0.0004 0.000 1.467 0.143 -0.000 0.001
Accounts Payable Capital Expenditures 4.251e-11 1.69e-11 2.522 0.012 9.44e-12 7.56e-11
Accounts Payable Capital Surplus 9.623e-13 3.53e-12 0.272 0.785 -5.97e-12 7.9e-12
Accounts Payable Cash Ratio 0.0002 0.000 0.518 0.604 -0.001 0.001
Accounts Payable Cash and Cash Equivalents -3.834e-12 6.16e-12 -0.622 0.534 -1.59e-11 8.26e-12
Accounts Payable Changes in Inventories 6.492e-13 2.05e-11 0.032 0.975 -3.95e-11 4.08e-11
Accounts Payable Common Stocks -4.705e-13 5.35e-12 -0.088 0.930 -1.1e-11 1e-11
Accounts Payable Cost of Revenue -2.524e-12 8.97e-13 -2.815 0.005 -4.28e-12 -7.65e-13
Accounts Payable Current Ratio 0.0004 0.000 1.532 0.126 -0.000 0.001
Accounts Payable Deferred Asset Charges -1.317e-11 1.39e-11 -0.949 0.343 -4.04e-11 1.41e-11
Accounts Payable Deferred Liability Charges 2.965e-12 1.03e-11 0.287 0.774 -1.73e-11 2.33e-11
Accounts Payable Depreciation -9.43e-11 2.63e-11 -3.591 0.000 -1.46e-10 -4.28e-11
Accounts Payable Earnings Before Interest and Tax -1.795e-10 6.49e-11 -2.764 0.006 -3.07e-10 -5.21e-11
Accounts Payable Earnings Before Tax 1.626e-10 6.51e-11 2.496 0.013 3.48e-11 2.9e-10
Accounts Payable Effect of Exchange Rate 4.771e-11 9.23e-11 0.517 0.605 -1.34e-10 2.29e-10
Accounts Payable Equity Earnings/Loss Unconsolidated Subsidiary 1.221e-10 8.19e-11 1.491 0.136 -3.86e-11 2.83e-10
Accounts Payable Fixed Assets 1.668e-11 3.4e-12 4.904 0.000 1e-11 2.34e-11
Accounts Payable Goodwill 1.292e-12 2.99e-12 0.432 0.666 -4.58e-12 7.17e-12
Accounts Payable Gross Margin -0.0003 0.000 -0.529 0.597 -0.001 0.001
Accounts Payable Gross Profit 8.664e-12 3e-12 2.886 0.004 2.77e-12 1.46e-11
Accounts Payable Income Tax 4.933e-11 3.55e-11 1.391 0.164 -2.02e-11 1.19e-10
Accounts Payable Intangible Assets 6.643e-12 5.37e-12 1.238 0.216 -3.89e-12 1.72e-11
Accounts Receivable^2 9.551e-11 3.46e-11 2.759 0.006 2.76e-11 1.63e-10
Accounts Receivable Add'l income/expense items -1.013e-10 1.5e-10 -0.674 0.500 -3.96e-10 1.93e-10
Accounts Receivable After Tax ROE -0.0005 0.002 -0.278 0.781 -0.004 0.003
Accounts Receivable Capital Expenditures -1.104e-10 6.89e-11 -1.603 0.109 -2.46e-10 2.47e-11
Accounts Receivable Capital Surplus -2.166e-12 1.23e-11 -0.176 0.860 -2.63e-11 2.2e-11
Accounts Receivable Cash Ratio -0.0055 0.002 -3.330 0.001 -0.009 -0.002
Accounts Receivable Cash and Cash Equivalents 1.292e-10 3.04e-11 4.244 0.000 6.95e-11 1.89e-10
Accounts Receivable Changes in Inventories -4.698e-12 1.12e-10 -0.042 0.966 -2.24e-10 2.14e-10
Accounts Receivable Common Stocks 4.173e-12 1.29e-11 0.323 0.747 -2.12e-11 2.95e-11
Accounts Receivable Cost of Revenue -6.611e-13 3.15e-12 -0.210 0.834 -6.85e-12 5.53e-12
Accounts Receivable Current Ratio 0.0024 0.001 2.130 0.033 0.000 0.005
Accounts Receivable Deferred Asset Charges -4.307e-11 5.67e-11 -0.760 0.447 -1.54e-10 6.81e-11
Accounts Receivable Deferred Liability Charges 4.377e-11 3.99e-11 1.097 0.273 -3.45e-11 1.22e-10
Accounts Receivable Depreciation -1.476e-10 9.46e-11 -1.561 0.119 -3.33e-10 3.8e-11
Accounts Receivable Earnings Before Interest and Tax -1.276e-10 1.61e-10 -0.795 0.427 -4.43e-10 1.88e-10
Accounts Receivable Earnings Before Tax 1.154e-10 1.63e-10 0.706 0.480 -2.05e-10 4.36e-10
Accounts Receivable Effect of Exchange Rate -4.757e-10 5.26e-10 -0.905 0.366 -1.51e-09 5.56e-10
Accounts Receivable Equity Earnings/Loss Unconsolidated Subsidiary 1.831e-10 2.09e-10 0.878 0.380 -2.26e-10 5.92e-10
Accounts Receivable Fixed Assets -1.09e-11 1.32e-11 -0.825 0.410 -3.68e-11 1.5e-11
Accounts Receivable Goodwill -8.104e-12 1.32e-11 -0.615 0.538 -3.39e-11 1.77e-11
Accounts Receivable Gross Margin 0.0066 0.003 2.114 0.035 0.000 0.013
Accounts Receivable Gross Profit 1.39e-11 1.22e-11 1.141 0.254 -9.99e-12 3.78e-11
Accounts Receivable Income Tax -6.825e-11 1.63e-10 -0.419 0.675 -3.88e-10 2.51e-10
Accounts Receivable Intangible Assets 2.752e-11 1.95e-11 1.408 0.159 -1.08e-11 6.59e-11
Add'l income/expense items^2 -7.035e-11 4.77e-11 -1.474 0.141 -1.64e-10 2.33e-11
Add'l income/expense items After Tax ROE -0.0021 0.002 -1.014 0.311 -0.006 0.002
Add'l income/expense items Capital Expenditures 1.908e-10 5.82e-11 3.277 0.001 7.65e-11 3.05e-10
Add'l income/expense items Capital Surplus -9.282e-13 1.34e-11 -0.069 0.945 -2.73e-11 2.54e-11
Add'l income/expense items Cash Ratio 0.0019 0.002 1.153 0.249 -0.001 0.005
Add'l income/expense items Cash and Cash Equivalents 3.723e-11 3.87e-11 0.961 0.337 -3.88e-11 1.13e-10
Add'l income/expense items Changes in Inventories -3.079e-10 3.38e-10 -0.912 0.362 -9.7e-10 3.54e-10
Add'l income/expense items Common Stocks -2.55e-11 2.61e-11 -0.975 0.330 -7.68e-11 2.58e-11
Add'l income/expense items Cost of Revenue 2.396e-12 7.36e-12 0.326 0.745 -1.2e-11 1.68e-11
Add'l income/expense items Current Ratio -0.0012 0.002 -0.792 0.428 -0.004 0.002
Add'l income/expense items Deferred Asset Charges -9.22e-11 8e-11 -1.153 0.249 -2.49e-10 6.47e-11
Add'l income/expense items Deferred Liability Charges -2.97e-11 2.04e-11 -1.454 0.146 -6.98e-11 1.04e-11
Add'l income/expense items Depreciation 6.248e-11 1.08e-10 0.577 0.564 -1.5e-10 2.75e-10
Add'l income/expense items Earnings Before Interest and Tax -1.056e-10 2.89e-10 -0.365 0.715 -6.73e-10 4.62e-10
Add'l income/expense items Earnings Before Tax 8.121e-11 2.82e-10 0.288 0.774 -4.73e-10 6.35e-10
Add'l income/expense items Effect of Exchange Rate -1.215e-09 3.83e-10 -3.170 0.002 -1.97e-09 -4.63e-10
Add'l income/expense items Equity Earnings/Loss Unconsolidated Subsidiary 3.101e-10 1.97e-10 1.578 0.115 -7.56e-11 6.96e-10
Add'l income/expense items Fixed Assets 3.413e-11 1.22e-11 2.797 0.005 1.02e-11 5.81e-11
Add'l income/expense items Goodwill 2.69e-11 1.81e-11 1.486 0.138 -8.62e-12 6.24e-11
Add'l income/expense items Gross Margin 0.0048 0.004 1.282 0.200 -0.003 0.012
Add'l income/expense items Gross Profit -4.31e-11 1.99e-11 -2.166 0.031 -8.22e-11 -4.04e-12
Add'l income/expense items Income Tax -8.883e-11 1.23e-10 -0.720 0.472 -3.31e-10 1.53e-10
Add'l income/expense items Intangible Assets 5.256e-12 2.22e-11 0.237 0.813 -3.83e-11 4.88e-11
After Tax ROE^2 -0.0005 0.001 -0.932 0.352 -0.002 0.001
After Tax ROE Capital Expenditures -0.0010 0.001 -1.464 0.144 -0.002 0.000
After Tax ROE Capital Surplus -1.243e-05 2.09e-05 -0.594 0.552 -5.35e-05 2.86e-05
After Tax ROE Cash Ratio -6.182e-06 7.93e-06 -0.779 0.436 -2.17e-05 9.38e-06
After Tax ROE Cash and Cash Equivalents 0.0001 0.000 0.574 0.566 -0.000 0.000
After Tax ROE Changes in Inventories -0.0044 0.001 -3.072 0.002 -0.007 -0.002
After Tax ROE Common Stocks -0.0005 0.001 -1.014 0.311 -0.002 0.000
After Tax ROE Cost of Revenue 0.0002 7.01e-05 2.663 0.008 4.91e-05 0.000
After Tax ROE Current Ratio -1.262e-05 1.23e-05 -1.022 0.307 -3.69e-05 1.16e-05
After Tax ROE Deferred Asset Charges -0.0039 0.001 -4.638 0.000 -0.006 -0.002
After Tax ROE Deferred Liability Charges 0.0002 0.001 0.410 0.682 -0.001 0.001
After Tax ROE Depreciation -0.0013 0.001 -1.878 0.061 -0.003 5.78e-05
After Tax ROE Earnings Before Interest and Tax -0.0018 0.002 -1.072 0.284 -0.005 0.001
After Tax ROE Earnings Before Tax 0.0024 0.002 1.333 0.183 -0.001 0.006
After Tax ROE Effect of Exchange Rate -0.0012 0.004 -0.337 0.736 -0.008 0.006
After Tax ROE Equity Earnings/Loss Unconsolidated Subsidiary -0.0066 0.004 -1.660 0.097 -0.014 0.001
After Tax ROE Fixed Assets -0.0003 0.000 -1.714 0.087 -0.001 3.84e-05
After Tax ROE Goodwill -0.0002 0.000 -0.947 0.344 -0.001 0.000
After Tax ROE Gross Margin -3.442e-06 4.15e-06 -0.829 0.407 -1.16e-05 4.71e-06
After Tax ROE Gross Profit -4.707e-05 0.000 -0.379 0.705 -0.000 0.000
After Tax ROE Income Tax -0.0017 0.001 -1.245 0.213 -0.004 0.001
After Tax ROE Intangible Assets 0.0004 0.000 1.596 0.111 -8.04e-05 0.001
Capital Expenditures^2 2.089e-11 8.93e-12 2.339 0.020 3.36e-12 3.84e-11
Capital Expenditures Capital Surplus -4.977e-13 6.18e-12 -0.080 0.936 -1.26e-11 1.16e-11
Capital Expenditures Cash Ratio 0.0026 0.001 2.749 0.006 0.001 0.004
Capital Expenditures Cash and Cash Equivalents -5.388e-11 2.19e-11 -2.465 0.014 -9.68e-11 -1.1e-11
Capital Expenditures Changes in Inventories 1.024e-11 1.06e-10 0.097 0.923 -1.97e-10 2.18e-10
Capital Expenditures Common Stocks 2.07e-11 1.24e-11 1.665 0.096 -3.69e-12 4.51e-11
Capital Expenditures Cost of Revenue -4.148e-12 3.24e-12 -1.281 0.200 -1.05e-11 2.21e-12
Capital Expenditures Current Ratio -0.0012 0.001 -1.925 0.055 -0.002 2.41e-05
Capital Expenditures Deferred Asset Charges -1.154e-11 3.82e-11 -0.302 0.763 -8.65e-11 6.34e-11
Capital Expenditures Deferred Liability Charges -4.592e-12 1.55e-11 -0.296 0.768 -3.51e-11 2.59e-11
Capital Expenditures Depreciation -2.458e-11 3.54e-11 -0.694 0.488 -9.4e-11 4.49e-11
Capital Expenditures Earnings Before Interest and Tax -6.934e-11 1.17e-10 -0.591 0.555 -3e-10 1.61e-10
Capital Expenditures Earnings Before Tax 7.589e-11 1.17e-10 0.651 0.515 -1.53e-10 3.05e-10
Capital Expenditures Effect of Exchange Rate -1.261e-09 4e-10 -3.155 0.002 -2.04e-09 -4.77e-10
Capital Expenditures Equity Earnings/Loss Unconsolidated Subsidiary 3.703e-10 1.06e-10 3.491 0.001 1.62e-10 5.78e-10
Capital Expenditures Fixed Assets 7.21e-12 5.15e-12 1.400 0.162 -2.9e-12 1.73e-11
Capital Expenditures Goodwill 3.401e-11 1.08e-11 3.147 0.002 1.28e-11 5.52e-11
Capital Expenditures Gross Margin 0.0021 0.001 1.517 0.130 -0.001 0.005
Capital Expenditures Gross Profit 2.73e-12 7.87e-12 0.347 0.729 -1.27e-11 1.82e-11
Capital Expenditures Income Tax -5.396e-11 5.67e-11 -0.952 0.341 -1.65e-10 5.73e-11
Capital Expenditures Intangible Assets -1.141e-10 1.87e-11 -6.118 0.000 -1.51e-10 -7.75e-11
Capital Surplus^2 1.784e-12 6.64e-13 2.687 0.007 4.81e-13 3.09e-12
Capital Surplus Cash Ratio 2.005e-05 0.000 0.189 0.850 -0.000 0.000
Capital Surplus Cash and Cash Equivalents 2.108e-12 3.16e-12 0.667 0.505 -4.09e-12 8.31e-12
Capital Surplus Changes in Inventories -2.655e-11 1.94e-11 -1.369 0.171 -6.46e-11 1.15e-11
Capital Surplus Common Stocks -5.717e-12 8.34e-12 -0.685 0.493 -2.21e-11 1.07e-11
Capital Surplus Cost of Revenue -1.598e-12 6.39e-13 -2.501 0.013 -2.85e-12 -3.44e-13
Capital Surplus Current Ratio 5.667e-05 8.69e-05 0.652 0.514 -0.000 0.000
Capital Surplus Deferred Asset Charges -2.37e-11 5.92e-12 -4.005 0.000 -3.53e-11 -1.21e-11
Capital Surplus Deferred Liability Charges -9.7e-12 3.41e-12 -2.843 0.005 -1.64e-11 -3e-12
Capital Surplus Depreciation -1.708e-11 1.06e-11 -1.604 0.109 -3.8e-11 3.81e-12
Capital Surplus Earnings Before Interest and Tax -6.221e-11 1.93e-11 -3.216 0.001 -1e-10 -2.42e-11
Capital Surplus Earnings Before Tax 5.253e-11 1.98e-11 2.651 0.008 1.36e-11 9.14e-11
Capital Surplus Effect of Exchange Rate -7.586e-12 4.44e-11 -0.171 0.864 -9.47e-11 7.96e-11
Capital Surplus Equity Earnings/Loss Unconsolidated Subsidiary -2.54e-11 3.29e-11 -0.771 0.441 -9e-11 3.92e-11
Capital Surplus Fixed Assets 3.835e-12 1.11e-12 3.444 0.001 1.65e-12 6.02e-12
Capital Surplus Goodwill -5.442e-12 1.51e-12 -3.615 0.000 -8.4e-12 -2.49e-12
Capital Surplus Gross Margin -0.0008 0.000 -2.678 0.008 -0.001 -0.000
Capital Surplus Gross Profit 3.447e-12 1.55e-12 2.228 0.026 4.12e-13 6.48e-12
Capital Surplus Income Tax -1.59e-11 1.23e-11 -1.293 0.196 -4e-11 8.23e-12
Capital Surplus Intangible Assets 9.538e-12 2.1e-12 4.541 0.000 5.42e-12 1.37e-11
Cash Ratio^2 2.642e-05 3.23e-05 0.818 0.414 -3.7e-05 8.98e-05
Cash Ratio Cash and Cash Equivalents 0.0002 0.000 0.696 0.487 -0.000 0.001
Cash Ratio Changes in Inventories -0.0012 0.003 -0.406 0.685 -0.007 0.005
Cash Ratio Common Stocks -0.0002 0.000 -0.848 0.397 -0.001 0.000
Cash Ratio Cost of Revenue -8.772e-07 0.000 -0.007 0.994 -0.000 0.000
Cash Ratio Current Ratio 1.414e-05 4.06e-05 0.348 0.728 -6.56e-05 9.39e-05
Cash Ratio Deferred Asset Charges -0.0017 0.001 -1.755 0.080 -0.003 0.000
Cash Ratio Deferred Liability Charges 0.0001 0.000 0.299 0.765 -0.001 0.001
Cash Ratio Depreciation 0.0029 0.001 2.154 0.031 0.000 0.006
Cash Ratio Earnings Before Interest and Tax -0.0047 0.003 -1.762 0.078 -0.010 0.001
Cash Ratio Earnings Before Tax 0.0048 0.003 1.782 0.075 -0.000 0.010
Cash Ratio Effect of Exchange Rate 0.0013 0.006 0.213 0.832 -0.010 0.013
Cash Ratio Equity Earnings/Loss Unconsolidated Subsidiary -0.0075 0.005 -1.601 0.110 -0.017 0.002
Cash Ratio Fixed Assets 0.0004 0.000 2.462 0.014 8.67e-05 0.001
Cash Ratio Goodwill 0.0003 0.000 1.964 0.050 3.49e-07 0.001
Cash Ratio Gross Margin -6.541e-06 7.04e-06 -0.929 0.353 -2.04e-05 7.28e-06
Cash Ratio Gross Profit -0.0005 0.000 -2.736 0.006 -0.001 -0.000
Cash Ratio Income Tax 0.0026 0.002 1.549 0.122 -0.001 0.006
Cash Ratio Intangible Assets -0.0007 0.000 -2.270 0.023 -0.001 -9.17e-05
Cash and Cash Equivalents^2 -6.367e-12 5.08e-12 -1.254 0.210 -1.63e-11 3.59e-12
Cash and Cash Equivalents Changes in Inventories -7.44e-11 5.4e-11 -1.377 0.169 -1.8e-10 3.17e-11
Cash and Cash Equivalents Common Stocks 9.151e-12 4.68e-12 1.955 0.051 -3.38e-14 1.83e-11
Cash and Cash Equivalents Cost of Revenue 1.179e-12 1.18e-12 0.999 0.318 -1.14e-12 3.5e-12
Cash and Cash Equivalents Current Ratio -0.0002 0.000 -0.631 0.528 -0.001 0.000
Cash and Cash Equivalents Deferred Asset Charges 6.149e-13 2.05e-11 0.030 0.976 -3.96e-11 4.08e-11
Cash and Cash Equivalents Deferred Liability Charges -1.819e-11 1.22e-11 -1.494 0.135 -4.21e-11 5.7e-12
Cash and Cash Equivalents Depreciation -2.805e-11 2.77e-11 -1.013 0.311 -8.24e-11 2.63e-11
Cash and Cash Equivalents Earnings Before Interest and Tax 8.079e-11 7.54e-11 1.071 0.284 -6.72e-11 2.29e-10
Cash and Cash Equivalents Earnings Before Tax -8.291e-11 7.63e-11 -1.086 0.278 -2.33e-10 6.69e-11
Cash and Cash Equivalents Effect of Exchange Rate -2.21e-10 1.1e-10 -2.003 0.045 -4.38e-10 -4.51e-12
Cash and Cash Equivalents Equity Earnings/Loss Unconsolidated Subsidiary 7.096e-13 9.12e-11 0.008 0.994 -1.78e-10 1.8e-10
Cash and Cash Equivalents Fixed Assets -7.376e-12 4.14e-12 -1.780 0.075 -1.55e-11 7.55e-13
Cash and Cash Equivalents Goodwill -8.812e-13 3.71e-12 -0.237 0.813 -8.17e-12 6.41e-12
Cash and Cash Equivalents Gross Margin 0.0014 0.001 2.084 0.037 8.45e-05 0.003
Cash and Cash Equivalents Gross Profit 6.773e-12 3.83e-12 1.768 0.077 -7.43e-13 1.43e-11
Cash and Cash Equivalents Income Tax -1.098e-10 3.89e-11 -2.826 0.005 -1.86e-10 -3.35e-11
Cash and Cash Equivalents Intangible Assets 9.485e-12 5.04e-12 1.881 0.060 -4.1e-13 1.94e-11
Changes in Inventories^2 8.666e-11 6.63e-11 1.307 0.191 -4.34e-11 2.17e-10
Changes in Inventories Common Stocks -6.249e-11 2.45e-11 -2.546 0.011 -1.11e-10 -1.43e-11
Changes in Inventories Cost of Revenue 5.377e-12 5e-12 1.075 0.283 -4.44e-12 1.52e-11
Changes in Inventories Current Ratio 0.0018 0.002 0.891 0.373 -0.002 0.006
Changes in Inventories Deferred Asset Charges 2.049e-10 6.92e-11 2.962 0.003 6.92e-11 3.41e-10
Changes in Inventories Deferred Liability Charges 1.487e-10 5.11e-11 2.910 0.004 4.84e-11 2.49e-10
Changes in Inventories Depreciation 4.553e-10 9.15e-11 4.975 0.000 2.76e-10 6.35e-10
Changes in Inventories Earnings Before Interest and Tax -5.347e-10 3.5e-10 -1.527 0.127 -1.22e-09 1.53e-10
Changes in Inventories Earnings Before Tax 7.132e-10 3.81e-10 1.872 0.062 -3.46e-11 1.46e-09
Changes in Inventories Effect of Exchange Rate -1.78e-11 7.17e-10 -0.025 0.980 -1.42e-09 1.39e-09
Changes in Inventories Equity Earnings/Loss Unconsolidated Subsidiary 7.696e-10 6.43e-10 1.197 0.232 -4.92e-10 2.03e-09
Changes in Inventories Fixed Assets -6.881e-11 1.82e-11 -3.791 0.000 -1.04e-10 -3.32e-11
Changes in Inventories Goodwill -4.452e-11 2.41e-11 -1.846 0.065 -9.18e-11 2.8e-12
Changes in Inventories Gross Margin 0.0023 0.007 0.326 0.745 -0.011 0.016
Changes in Inventories Gross Profit -3.772e-11 2.15e-11 -1.754 0.080 -7.99e-11 4.49e-12
Changes in Inventories Income Tax 1.63e-10 2.54e-10 0.641 0.522 -3.36e-10 6.62e-10
Changes in Inventories Intangible Assets -5.129e-11 3.8e-11 -1.348 0.178 -1.26e-10 2.34e-11
Common Stocks^2 1.634e-12 2.14e-12 0.762 0.446 -2.58e-12 5.84e-12
Common Stocks Cost of Revenue -1.325e-12 1.79e-12 -0.741 0.459 -4.83e-12 2.18e-12
Common Stocks Current Ratio 0.0002 0.000 1.173 0.241 -0.000 0.001
Common Stocks Deferred Asset Charges -3.641e-12 7.21e-12 -0.505 0.614 -1.78e-11 1.05e-11
Common Stocks Deferred Liability Charges 5.385e-12 5.73e-12 0.940 0.347 -5.85e-12 1.66e-11
Common Stocks Depreciation 6.241e-12 1.81e-11 0.345 0.730 -2.93e-11 4.17e-11
Common Stocks Earnings Before Interest and Tax 1.08e-10 3.93e-11 2.748 0.006 3.09e-11 1.85e-10
Common Stocks Earnings Before Tax -1.047e-10 3.93e-11 -2.663 0.008 -1.82e-10 -2.75e-11
Common Stocks Effect of Exchange Rate 4.359e-13 6.65e-11 0.007 0.995 -1.3e-10 1.31e-10
Common Stocks Equity Earnings/Loss Unconsolidated Subsidiary -9.268e-11 8.02e-11 -1.156 0.248 -2.5e-10 6.47e-11
Common Stocks Fixed Assets 1.257e-12 2.05e-12 0.612 0.541 -2.77e-12 5.29e-12
Common Stocks Goodwill -5.272e-13 2.26e-12 -0.233 0.816 -4.97e-12 3.92e-12
Common Stocks Gross Margin 0.0001 0.001 0.180 0.857 -0.001 0.002
Common Stocks Gross Profit 1.329e-12 4.25e-12 0.313 0.754 -7.01e-12 9.67e-12
Common Stocks Income Tax -2.192e-11 1.55e-11 -1.414 0.158 -5.23e-11 8.5e-12
Common Stocks Intangible Assets -1.819e-11 3.6e-12 -5.049 0.000 -2.53e-11 -1.11e-11
Cost of Revenue^2 2.738e-13 1.14e-13 2.398 0.017 4.97e-14 4.98e-13
Cost of Revenue Current Ratio 2.922e-05 5.15e-05 0.567 0.571 -7.19e-05 0.000
Cost of Revenue Deferred Asset Charges 2.916e-12 3.52e-12 0.828 0.408 -4e-12 9.83e-12
Cost of Revenue Deferred Liability Charges 1.478e-12 1.72e-12 0.858 0.391 -1.9e-12 4.86e-12
Cost of Revenue Depreciation 2.738e-11 7.72e-12 3.549 0.000 1.22e-11 4.25e-11
Cost of Revenue Earnings Before Interest and Tax 3.264e-11 1.32e-11 2.480 0.013 6.81e-12 5.85e-11
Cost of Revenue Earnings Before Tax -3.502e-11 1.32e-11 -2.663 0.008 -6.08e-11 -9.21e-12
Cost of Revenue Effect of Exchange Rate 6.416e-12 1.58e-11 0.405 0.685 -2.47e-11 3.75e-11
Cost of Revenue Equity Earnings/Loss Unconsolidated Subsidiary -8.37e-12 7.55e-12 -1.109 0.268 -2.32e-11 6.44e-12
Cost of Revenue Fixed Assets -3.427e-12 7.66e-13 -4.471 0.000 -4.93e-12 -1.92e-12
Cost of Revenue Goodwill 1.197e-14 6.96e-13 0.017 0.986 -1.35e-12 1.38e-12
Cost of Revenue Gross Margin 8.923e-05 0.001 0.111 0.911 -0.001 0.002
Cost of Revenue Gross Profit -1.447e-12 6.82e-13 -2.122 0.034 -2.79e-12 -1.09e-13
Cost of Revenue Income Tax 1.603e-11 6.19e-12 2.588 0.010 3.88e-12 2.82e-11
Cost of Revenue Intangible Assets 5.827e-13 1.21e-12 0.480 0.631 -1.8e-12 2.96e-12
Current Ratio^2 -7.804e-05 8.56e-05 -0.911 0.362 -0.000 9e-05
Current Ratio Deferred Asset Charges 0.0006 0.001 1.171 0.242 -0.000 0.002
Current Ratio Deferred Liability Charges 0.0001 0.000 0.380 0.704 -0.001 0.001
Current Ratio Depreciation -0.0027 0.001 -3.301 0.001 -0.004 -0.001
Current Ratio Earnings Before Interest and Tax 0.0011 0.002 0.663 0.507 -0.002 0.004
Current Ratio Earnings Before Tax -0.0004 0.002 -0.246 0.806 -0.004 0.003
Current Ratio Effect of Exchange Rate 0.0062 0.004 1.689 0.091 -0.001 0.013
Current Ratio Equity Earnings/Loss Unconsolidated Subsidiary 0.0018 0.003 0.578 0.564 -0.004 0.008
Current Ratio Fixed Assets -0.0001 0.000 -0.950 0.342 -0.000 0.000
Current Ratio Goodwill -0.0003 0.000 -1.725 0.085 -0.001 3.48e-05
Current Ratio Gross Margin -1.839e-05 9.52e-06 -1.931 0.054 -3.71e-05 2.95e-07
Current Ratio Gross Profit 0.0002 0.000 1.803 0.072 -2.02e-05 0.000
Current Ratio Income Tax -0.0033 0.001 -2.338 0.020 -0.006 -0.001
Current Ratio Intangible Assets 0.0002 0.000 1.062 0.289 -0.000 0.001
Deferred Asset Charges^2 -2.533e-12 1.79e-11 -0.141 0.888 -3.77e-11 3.27e-11
Deferred Asset Charges Deferred Liability Charges -9.369e-12 1.81e-11 -0.517 0.605 -4.49e-11 2.62e-11
Deferred Asset Charges Depreciation 7.728e-12 6.03e-11 0.128 0.898 -1.11e-10 1.26e-10
Deferred Asset Charges Earnings Before Interest and Tax -5.642e-11 1.49e-10 -0.377 0.706 -3.5e-10 2.37e-10
Deferred Asset Charges Earnings Before Tax 7.956e-11 1.49e-10 0.533 0.594 -2.13e-10 3.72e-10
Deferred Asset Charges Effect of Exchange Rate 2.067e-10 1.86e-10 1.114 0.266 -1.57e-10 5.71e-10
Deferred Asset Charges Equity Earnings/Loss Unconsolidated Subsidiary 2.912e-10 1.96e-10 1.484 0.138 -9.38e-11 6.76e-10
Deferred Asset Charges Fixed Assets -4.394e-13 7.05e-12 -0.062 0.950 -1.43e-11 1.34e-11
Deferred Asset Charges Goodwill -1.453e-11 8.47e-12 -1.714 0.087 -3.12e-11 2.1e-12
Deferred Asset Charges Gross Margin 0.0017 0.002 0.738 0.461 -0.003 0.006
Deferred Asset Charges Gross Profit 6.418e-12 6.92e-12 0.928 0.354 -7.16e-12 2e-11
Deferred Asset Charges Income Tax -1.672e-11 6.71e-11 -0.249 0.803 -1.48e-10 1.15e-10
Deferred Asset Charges Intangible Assets 2.316e-11 1.45e-11 1.593 0.111 -5.36e-12 5.17e-11
Deferred Liability Charges^2 9.042e-12 4.93e-12 1.835 0.067 -6.27e-13 1.87e-11
Deferred Liability Charges Depreciation 2.121e-11 2.62e-11 0.811 0.418 -3.01e-11 7.26e-11
Deferred Liability Charges Earnings Before Interest and Tax -9.599e-11 6.02e-11 -1.595 0.111 -2.14e-10 2.21e-11
Deferred Liability Charges Earnings Before Tax 9.343e-11 5.96e-11 1.568 0.117 -2.35e-11 2.1e-10
Deferred Liability Charges Effect of Exchange Rate -5.026e-10 1.78e-10 -2.820 0.005 -8.52e-10 -1.53e-10
Deferred Liability Charges Equity Earnings/Loss Unconsolidated Subsidiary 8.816e-11 8.13e-11 1.084 0.279 -7.15e-11 2.48e-10
Deferred Liability Charges Fixed Assets -3.031e-12 2.75e-12 -1.101 0.271 -8.43e-12 2.37e-12
Deferred Liability Charges Goodwill 4.869e-12 5.12e-12 0.951 0.342 -5.18e-12 1.49e-11
Deferred Liability Charges Gross Margin 0.0007 0.001 0.751 0.453 -0.001 0.003
Deferred Liability Charges Gross Profit -3.769e-12 4.45e-12 -0.847 0.397 -1.25e-11 4.97e-12
Deferred Liability Charges Income Tax 1.916e-11 4.03e-11 0.476 0.634 -5.99e-11 9.82e-11
Deferred Liability Charges Intangible Assets -5.091e-12 6.28e-12 -0.810 0.418 -1.74e-11 7.24e-12
Depreciation^2 9.337e-11 2.67e-11 3.495 0.000 4.09e-11 1.46e-10
Depreciation Earnings Before Interest and Tax -1.65e-10 1.65e-10 -0.998 0.318 -4.89e-10 1.59e-10
Depreciation Earnings Before Tax 2.076e-10 1.69e-10 1.229 0.219 -1.24e-10 5.39e-10
Depreciation Effect of Exchange Rate -9.583e-10 4.87e-10 -1.969 0.049 -1.91e-09 -3.26e-12
Depreciation Equity Earnings/Loss Unconsolidated Subsidiary 2.611e-10 2.23e-10 1.171 0.242 -1.77e-10 6.99e-10
Depreciation Fixed Assets -3.167e-11 7.26e-12 -4.365 0.000 -4.59e-11 -1.74e-11
Depreciation Goodwill 6.262e-11 1.34e-11 4.661 0.000 3.63e-11 8.9e-11
Depreciation Gross Margin 0.0095 0.002 3.871 0.000 0.005 0.014
Depreciation Gross Profit -2.166e-11 1.53e-11 -1.414 0.158 -5.17e-11 8.39e-12
Depreciation Income Tax -1.233e-11 9.92e-11 -0.124 0.901 -2.07e-10 1.82e-10
Depreciation Intangible Assets -4.768e-11 1.59e-11 -3.001 0.003 -7.89e-11 -1.65e-11
Earnings Before Interest and Tax^2 -6.361e-11 2.49e-10 -0.256 0.798 -5.52e-10 4.25e-10
Earnings Before Interest and Tax Earnings Before Tax 1.371e-10 4.94e-10 0.277 0.781 -8.33e-10 1.11e-09
Earnings Before Interest and Tax Effect of Exchange Rate -6.46e-10 8.54e-10 -0.756 0.450 -2.32e-09 1.03e-09
Earnings Before Interest and Tax Equity Earnings/Loss Unconsolidated Subsidiary 2.285e-10 5.91e-10 0.387 0.699 -9.31e-10 1.39e-09
Earnings Before Interest and Tax Fixed Assets 1.562e-11 2.12e-11 0.738 0.461 -2.59e-11 5.72e-11
Earnings Before Interest and Tax Goodwill -9.624e-11 3.09e-11 -3.115 0.002 -1.57e-10 -3.56e-11
Earnings Before Interest and Tax Gross Margin -0.0002 0.005 -0.050 0.960 -0.010 0.009
Earnings Before Interest and Tax Gross Profit -3.139e-11 2.85e-11 -1.102 0.271 -8.73e-11 2.45e-11
Earnings Before Interest and Tax Income Tax -4.619e-10 3.06e-10 -1.510 0.131 -1.06e-09 1.38e-10
Earnings Before Interest and Tax Intangible Assets 1.747e-10 4.36e-11 4.006 0.000 8.91e-11 2.6e-10
Earnings Before Tax^2 -6.858e-11 2.56e-10 -0.268 0.789 -5.71e-10 4.34e-10
Earnings Before Tax Effect of Exchange Rate 9.006e-10 8.99e-10 1.002 0.317 -8.63e-10 2.66e-09
Earnings Before Tax Equity Earnings/Loss Unconsolidated Subsidiary 1.594e-10 6.17e-10 0.259 0.796 -1.05e-09 1.37e-09
Earnings Before Tax Fixed Assets -1.341e-11 2.12e-11 -0.631 0.528 -5.51e-11 2.83e-11
Earnings Before Tax Goodwill 9.039e-11 3.12e-11 2.896 0.004 2.91e-11 1.52e-10
Earnings Before Tax Gross Margin -7.03e-05 0.005 -0.014 0.989 -0.010 0.010
Earnings Before Tax Gross Profit 2.733e-11 2.88e-11 0.950 0.342 -2.91e-11 8.38e-11
Earnings Before Tax Income Tax 4.556e-10 3.07e-10 1.483 0.139 -1.47e-10 1.06e-09
Earnings Before Tax Intangible Assets -1.504e-10 4.33e-11 -3.473 0.001 -2.35e-10 -6.54e-11
Effect of Exchange Rate^2 2.324e-09 9.55e-10 2.433 0.015 4.5e-10 4.2e-09
Effect of Exchange Rate Equity Earnings/Loss Unconsolidated Subsidiary -8.245e-10 1.16e-09 -0.714 0.476 -3.09e-09 1.44e-09
Effect of Exchange Rate Fixed Assets 3.947e-11 5.59e-11 0.706 0.481 -7.03e-11 1.49e-10
Effect of Exchange Rate Goodwill 4.162e-11 6.2e-11 0.671 0.502 -8e-11 1.63e-10
Effect of Exchange Rate Gross Margin 0.0028 0.010 0.278 0.781 -0.017 0.022
Effect of Exchange Rate Gross Profit -1.295e-10 5.5e-11 -2.354 0.019 -2.37e-10 -2.15e-11
Effect of Exchange Rate Income Tax -6.812e-10 5.17e-10 -1.318 0.188 -1.7e-09 3.33e-10
Effect of Exchange Rate Intangible Assets 3.966e-10 1e-10 3.961 0.000 2e-10 5.93e-10
Equity Earnings/Loss Unconsolidated Subsidiary^2 1.587e-10 1.75e-10 0.906 0.365 -1.85e-10 5.02e-10
Equity Earnings/Loss Unconsolidated Subsidiary Fixed Assets -4.28e-13 2.81e-11 -0.015 0.988 -5.56e-11 5.47e-11
Equity Earnings/Loss Unconsolidated Subsidiary Goodwill 1.059e-10 6.35e-11 1.670 0.095 -1.86e-11 2.3e-10
Equity Earnings/Loss Unconsolidated Subsidiary Gross Margin 0.0126 0.008 1.643 0.101 -0.002 0.028
Equity Earnings/Loss Unconsolidated Subsidiary Gross Profit -6.381e-11 4.96e-11 -1.287 0.199 -1.61e-10 3.35e-11
Equity Earnings/Loss Unconsolidated Subsidiary Income Tax -7.514e-10 2.91e-10 -2.583 0.010 -1.32e-09 -1.81e-10
Equity Earnings/Loss Unconsolidated Subsidiary Intangible Assets -4.854e-12 4.27e-11 -0.114 0.910 -8.87e-11 7.9e-11
Fixed Assets^2 1.593e-12 5.87e-13 2.715 0.007 4.42e-13 2.74e-12
Fixed Assets Goodwill 3.834e-12 1.75e-12 2.186 0.029 3.92e-13 7.28e-12
Fixed Assets Gross Margin -0.0003 0.000 -0.899 0.369 -0.001 0.000
Fixed Assets Gross Profit 2.089e-12 1.83e-12 1.142 0.254 -1.5e-12 5.68e-12
Fixed Assets Income Tax -2.051e-11 1.41e-11 -1.459 0.145 -4.81e-11 7.08e-12
Fixed Assets Intangible Assets -1.632e-11 2.94e-12 -5.558 0.000 -2.21e-11 -1.06e-11
Goodwill^2 -1.841e-12 1.29e-12 -1.422 0.155 -4.38e-12 6.99e-13
Goodwill Gross Margin 0.0003 0.000 0.641 0.522 -0.001 0.001
Goodwill Gross Profit -7.55e-12 2.5e-12 -3.017 0.003 -1.25e-11 -2.64e-12
Goodwill Income Tax 5.089e-11 2.15e-11 2.368 0.018 8.73e-12 9.31e-11
Goodwill Intangible Assets 6.023e-12 2.43e-12 2.480 0.013 1.26e-12 1.08e-11
Gross Margin^2 -5.652e-06 3.7e-06 -1.527 0.127 -1.29e-05 1.61e-06
Gross Margin Gross Profit -0.0005 0.001 -0.544 0.586 -0.002 0.001
Gross Margin Income Tax 0.0019 0.004 0.472 0.637 -0.006 0.010
Gross Margin Intangible Assets 0.0011 0.001 1.633 0.103 -0.000 0.002
Gross Profit^2 -7.117e-14 9.31e-13 -0.076 0.939 -1.9e-12 1.76e-12
Gross Profit Income Tax 1.632e-11 1.43e-11 1.140 0.254 -1.18e-11 4.44e-11
Gross Profit Intangible Assets 2.609e-12 3.12e-12 0.836 0.403 -3.51e-12 8.73e-12
Income Tax^2 1.477e-11 3.84e-11 0.385 0.700 -6.05e-11 9e-11
Income Tax Intangible Assets -5.086e-11 2.26e-11 -2.253 0.024 -9.52e-11 -6.56e-12
Intangible Assets^2 -6.585e-12 2.24e-12 -2.939 0.003 -1.1e-11 -2.19e-12
==============================================================================
Omnibus: 712.870 Durbin-Watson: 1.445
Prob(Omnibus): 0.000 Jarque-Bera (JB): 19521.497
Skew: 1.999 Prob(JB): 0.00
Kurtosis: 21.566 Cond. No. 3.07e+16
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 3.07e+16. This might indicate that there are
strong multicollinearity or other numerical problems.
Insights: High R-squared Value : The model has a high R-squared value (0.944), indicating that it explains a significant portion of the variance in the dependent variable. This suggests strong predictive power but also raises concerns about potential overfitting due to the model's complexity. Risk of Multicollinearity : The presence of a high condition number signals potential multicollinearity issues among the predictor variables. This can lead to unstable estimates of coefficients. Significant Variables : Some predictors show statistical significance (e.g., 'Capital Surplus', 'Intangible Assets'). These variables are likely to have a more substantial impact on the dependent variable.
7 [b] Briefly explain why interaction terms might be important in the context of predicting Estimated Shares Outstanding using fundamental financial metrics.
"""
Interaction terms help in creating a more accurate model by considering the combined impact of multiple financial metrics.
Interaction terms can uncover hidden patterns and relationships in financial data that single metrics might miss.
They enable the model to reflect the complex and often non-linear relationships between different financial metrics.
Including these terms can significantly improve the model's ability to predict outcomes in a complex financial landscape.
They account for non-linear interactions between variables, a common scenario in financial data.
Understanding these complex interactions aids in more effective financial planning and strategy formulation.
For analysts and decision-makers, these terms provide a more nuanced understanding of financial dynamics, aiding in better strategic decisions.
"""
Evaluating the performance of this new model with interaction terms. Compare it with the performance of the original model without interaction terms using appropriate metrics.
""" 1. R-squared and Adjusted R-squared: Model with Interaction Terms (Model 2) : R-squared of 0.944 and Adjusted R-squared of 0.926. Model without Interaction Terms (Model 1) : R-squared of 0.854 and Adjusted R-squared of 0.846. 2. F-statistic: Model 2 : F-statistic of 52.58. Model 1 : F-statistic of 98.40 3. Model Complexity: Model 2 : Much more complex with 315 predictors. Model 1 : Simpler with 73 predictors 4. AIC Model 2 : AIC = 5.440e+04. Model 1 : AIC = 5.516e+04. """
Any significant changes in the model's performance or the coefficients of the predictors
Model 2 shows a higher R-squared and Adjusted R-squared, indicating it explains more variability of the dependent variable and has a better overall fit, even after adjusting for the number of predictors. Although Model 1 has a higher F-statistic, indicating a stronger overall statistical significance, the F-statistic must be interpreted in the context of the number of predictors. Model 2, despite a lower F-statistic, deals with a more complex model (more predictors). P-values of the Coefficients: Both Models : Contain a mix of significant and non-significant p-values. The significance of individual predictors should be assessed, especially in Model 2 where the interaction terms add complexity. Some coefficients might be significant in one model but not in the other, indicating the importance of interaction effects. While Model 2 might capture more nuanced relationships due to interaction terms, its complexity can make it harder to interpret and might risk overfitting. Model 2 has a lower AIC, suggesting it is a better model in terms of the trade-off between goodness of fit and complexity. Like AIC, lower BIC values indicate a better model, but BIC penalizes the number of parameters more heavily. Model 1 has a lower BIC, suggesting that when accounting for the higher penalty on model complexity, the original model without interaction terms might be more preferable.
FDR Analysis with Interaction Terms: Create a histogram of the p-values for the new model including interaction terms. Discuss any noticeable differences from the histogram you created for the original model
# histogram of p-values
plt.hist(interaction_model.pvalues, bins=20, edgecolor='black')
plt.title('Histogram of P-Values')
plt.xlabel('P-Value')
plt.ylabel('Frequency')
plt.show()
"""The histogram showing a high number of p-values close to zero in the model with interaction terms implies that many predictors, both main effects and interactions, have statistical significance. This suggests that adding interaction terms effectively captures more relevant relationships between variables."""
Applying the Benjamini-Hochberg (BH) procedure to control the False Discovery Rate
(FDR) with a q-value of 0.1. How many significant predictors are identified now,
including both main effects and interaction effects.
# when q = 0.1
num_of_true_discoveries_intr, alpha1 = fdr(interaction_model.pvalues, 0.10, plotit=True)
print(f"When q= 0.1 \n"
f"The alpha is: {alpha1} \n"
f"The estimated number of true discoveries for interaction: {num_of_true_discoveries_intr}")
Alpha: 0.01957029918967793
When q= 0.1 The alpha is: 0.01957029918967793 The estimated number of true discoveries for interaction: 74
#without interaction
num_of_true_discoveries, alpha = fdr(model.pvalues, 0.1, plotit=True)
print(f"No. of true discoveries: {num_of_true_discoveries}")
Alpha: 0.001686631337479228
No. of true discoveries: 7
Compare these results with those obtained from the original model. Discuss the impact of including interaction terms on the number of discoveries and the control of the FDR
""" 1. The enhanced model with interaction terms identified a significantly higher number of true discoveries (75) compared to the base model (7), highlighting the effectiveness of interaction terms in revealing more complex relationships.
2. Alpha values are relatively consistent between the two models, with the new model showing a slightly higher threshold (0.0195) for determining statistical significance compared to the original model (0.0168).
3. The concentration of low p-values near zero in the histogram for the new model indicates a robust number of significant predictors, suggesting a better model fit due to the inclusion of interaction terms.
4. More predictors fall below the false discovery rate line in the new model's histogram, signifying a greater detection of significant relationships without substantially increasing the rate of false discoveries.
5. While the distribution of p-values in the new model suggests a strong fit, it also necessitates careful consideration of potential overfitting, which should be examined with additional validation techniques."""